ADI finite difference schemes for the Heston-Hull-White PDE
Abstract
In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider the Heston-Hull-White model with arbitrary correlation factors, with time-dependent mean-reversion levels, with short and long maturities, for cases where the Feller condition is satisfied and for cases where it is not. In addition, both European-style call options and up-and-out call options are considered. It is shown through extensive tests that ADI schemes, with a proper choice of their parameters, perform very well in all situations - in terms of stability, accuracy and efficiency.
Keywords
Cite
@article{arxiv.1111.4087,
title = {ADI finite difference schemes for the Heston-Hull-White PDE},
author = {Tinne Haentjens and Karel J. in 't Hout},
journal= {arXiv preprint arXiv:1111.4087},
year = {2013}
}